Why is the hypothesis test for an OLS parameter estimate a t-test when o is unknown, and yet you know that the asymptotic distribution of the parameter estimates are Normally distributed? Prove...

Extracted text: Why is the hypothesis test for an OLS parameter estimate a t-test when o is unknown, and yet you know that the asymptotic distribution of the parameter estimates are Normally distributed? Prove definitively. Why is the goodness of fit test of your OLS model an F-test? Prove definitively.